• Journal of the Korean Society for Precision Engineering
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• v.10 no.1
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• pp.89-99
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• 1993

A solid modeller was developed in this paper. Representation scheme of modelling is nonmanifold B-rep. While namy B-rep modellers use edges as basic element of modelling, this modeller is triangle-based. New modelling element, split triangle that is composed of 3 pure half-edges and has no information about the adjoining triangles, was defined to enlarge the range of representation. Corresponding algorithms for Boolean set operations were also developed.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1423-1431
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• 2015

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number is the minimum cardinality of a clique-transversal set in G. For every cubic graph with at most two bridges, we first show that it has a perfect matching which contains exactly one edge of each triangle of it; by the result, we determine the exact value of the clique-transversal number of line graph of it. Also, we present a sharp upper bound on the clique-transversal number of line graph of a cubic graph. Furthermore, we prove that the clique-transversal number of line graph of a triangle-free graph is at most the chromatic number of complement of the triangle-free graph.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.101-113
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• 2008

Let M be an arbitrary module over a commutative Noetherian ring R and let ${\triangle}$ be a multiplicatively closed set of non-zero ideals of R. In this paper, we will introduce the dual notion of ${\triangle}$-closure and ${\triangle}$-dependence of an ideal with respect to M and obtain some related results.

• Journal of the Korea Computer Graphics Society
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• v.17 no.3
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• pp.9-19
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• 2011

Computing triangle-triangle intersections has been a fundamental task required for many 3D geometric problems. We propose a novel robust GPU algorithm to efficiently compute intersections in a large triangle set. The algorithm has three stages:k-d tree construction, triangle pair generation, and exact intersection computation. All three stages are executed on GPU except, for unsafe triangle pairs. Unsafe triangle pairs are robustly handled by CLP(controlled linear perturbation) on a CPU thread. They are identified by floating-point filtering while exact intersection is computed on GPU. Many triangles crossing a split plane are duplicated in k-d tree construction, which form a lot of redundant triangle pairs later. To eliminate them efficiently, we use a split index which can determine redundancy of a pair by a simple bitwise operation. We applied the proposed algorithm to computing 3D Minkowski sum boundaries to verify its efficiency and robustness.

• Journal of ILASS-Korea
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• v.13 no.1
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• pp.9-15
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• 2008

This experimental study was carried out to examine the heat transfer characteristics of impinging air jet on a flat plate with a set of right angled triangle rods. Each right angled triangle rod in the array was positioned normal to the flow direction and parallel to the flat plate surface. The clearances from a right angled triangle rod to flat plate surface (C=1, 2 and 4 mm) and the distance from nozzle exit to flat plate (H=100 and 500 mm) were changed for the pitch between each right angled triangle rods (P=40 mm). As a result, heat transfer shows best performance at the clearance of C=1 mm, in case clearance changed, and the average heat transfer enhancement rate increased up to 47% compared to the result of a flat plate without a right angled triangle rod.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.787-811
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• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.

• Journal of Information Processing Systems
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• v.13 no.4
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• pp.818-833
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• 2017

This paper introduces a new algorithm that renders motion blur using triangular motion paths. A triangle occupies a set of pixels when moving from a position in the start of a frame to another position in the end of a frame. This is a motion path of a moving triangle. For a given pixel, we use a motion path of each moving triangle to find a range of time that this moving triangle is visible to the camera. Then, we sort visible time ranges in the depth-time dimensions and use bitwise operations to solve the occlusion problem. Thereafter, we compute an average color of each moving triangle based on its visible time range. Finally, we accumulate an average color of each moving triangle in the front-to-back order to produce the final pixel color. Thus, our algorithm performs shading after the visibility test and renders motion blur in real time.

• Journal of the Korean Society of Costume
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• v.35
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• pp.305-324
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• 1997

The purpose of this study was to examine aesthetic effects of face type and necklines of one piece dress one of details in clothes on visual evaluation. For this study two set of stages were processed. At first stage data were collected from female college students in Kwang Ju.Chonnam. Subjects between the aged of 18-26 were took pictured of their faces then they were classified into 7 groups That is egg ob-long round square inverted triangle triangle and diamond shapes. At second stage two sets of experimental design were utilized based on the classified face types. A set of design was 5$\times$4 design which involved 5 levels (egg oblong round inverted triangle and diamong shape) of face type and 4 levels(round boat vee and square neckline) of basic neckline. Another set of de-sign also was 5$\times$4 design which involved 5 levels of face type and 4 levels of modified neckline. As experimental treatment the stimulus materials and questionnaires were employed. The qustionnaires were consisted of visual evaluations on the stimulus materials by using semantic differential scale,. The experiments were proceeded through 2 week by 30 subjects composed of gaduate students and staffs in some departments of Clothing and Textiles at college. Data were analyzed by Frequencies Mean Factor Analysis TTest ANOVA and Ducan's Multiple Range Test. The major results were as followed: 1. There were significant aesthetic effects of face type on visual evaluations, Especially egg and inverted triangle shape among the face types were evaluated more aesthetic than the other face shapes. 2. There were signifiant aesthetic effects of the neckline types on visual evaluations, Es-pecially vee neckline among necklines were more aesthetic than the other necklines,. 3. As compared with the basic neckline types and the modified neckline types the modified necklines were assessed more aes-thetically than the basic necklines. 4, The face type and he neckline type were influenced interactively on visual evauations Specifically it showed that oblong round and diamond shape of face type were matched to vee neckline more than the other necklines, Also it showed that the egg and inverted tri-angle shape wee matched to round vee and squre neckline more than boat neckline.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.41-44
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• 2001

In reverse engineering, the whole surfaces of the three-dimensional(3D) product are measured using 3D positional scanners. The raw triangle meshes constructed from a scanned point set are not well suited for direct use in the downstream activities. This is because the amount of triangle meshes may be very large(from millions to hundreds of millions) and usually distorted by scanning error. Furthermore, the triangle meshes may contain several holes that must be filled. Thus, several solutions have to be addressed and implemented before a complete CAD models can be acquired. This paper discusses on the algorithms of decimation, smoothing, and hole-filling that are crucial to refine the triangle meshes. Several examples are also given and discussed to validate the system.

• Korean Journal of Computational Design and Engineering
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• v.17 no.4
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• pp.262-273
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• 2012

We present a novel GPU algorithm to compute outer cell boundaries of 3D arrangement subdivided by a given set of triangles. An outer cell boundary is defined as a 2-manifold surface consisting of subdivided polygons facing outward. Many geometric problems, such as Minkowski sum, sweep volume, lower/upper envelop, Bool operations, can be reduced to finding outer cell boundaries with specific properties. Computing outer cell boundaries, however, is a very time-consuming job and also is susceptible to numerical errors. To address these problems, we develop an algorithm based on GPU with a robust scheme combining interval arithmetic and multi-level precisions. The proposed algorithm is tested on Minkowski sum of several polygonal models, and shows 5-20 times speedup over an existing algorithm running on CPU.